Tilted Forum Project Discussion Community  

Go Back   Tilted Forum Project Discussion Community > The Academy > Tilted Knowledge and How-To


 
 
LinkBack Thread Tools
Old 03-12-2005, 10:34 AM   #1 (permalink)
Psycho
 
essendoubleop's Avatar
 
Matrix word problems

How would I set up these problems into a matrix? I can probably solve from there.

1)Jack is investing $50,000 in three mutual funds. He estimates that the money market fund will return 5% over the next year, the blue-chip fund will return 9%, and the high-tech fund 16%. He wants a total first-year return of $4000. To avoid excessive risk, he decides to invest three times as much in the money-market fund as in the high-tech fund. How much should Jack invest in each fund?

2)Suppose you work for a supplier of lawn products. The company needs to ship 600 pounds of grass fertilizer with a nitrogen content of 25%. You check the warehouse and find they don't have any 25% nitrogen fertilizer in stock. The warehouse has on hand three different types of grass fertilizer, G1, G2, G3, with nitrogen contents of 30%, 20%, and 15% respectively. Your boss says, "Figure out how to mix them to get the 600 pounds." You reply, "Boss, I've got three variables but only two equations. There's going to be a lot of solutions." The boss answers, "I don't care how you do it as long as you use full sacks. I don't want any open sacks hanging around to spill." Fertilizer G3 is in 60 pound sacks and the other two are in 30 pound sacks. List ALL of the various ways you can mix the fertilizers. (For instance, 10 sacks of G1 and 10 sacks of G2 is one way.)
essendoubleop is offline  
Old 03-18-2005, 12:48 PM   #2 (permalink)
Insane
 
yatzr's Avatar
 
okay, for the first one:
I'll call the variables M1, M2, M3 = money market, blue-chip, high-tech in that order
you've been given 3 equations

50,000 = M1 + M2 + M3
4,000 = .05*M1 + .09*M2 + .16*M3
M1 = 3*M3 or 0 = M1 - 3*M3

From this we have Ax=y where y is the matrix (or vector):

|50,000|
| 4,000|
| 0 |

A is the matrix:
| 1 1 1 |
| .05 .09 .16 |
| 1 0 -3 |

x is the matrix (or vector)
|M1|
|M2|
|M3|

you should be able to solve from there.



for problem 2:
Your two equations are:

600 = 30*G1 + 30*G2 + 60*G3
.25*600 = .3*30*G1 + .2*30*G2 + .15*60*G3

(for the second equation, it was easier to think of it in total amount of nitrogen instead of percentages which is why I did it that way)
from there you again have Ax=y
y is:
|600|
|150|

A is:
|30 30 60|
|9 6 9 |

xis:
|G1|
|G2|
|G3|

if you need any help solving them, just make the augmented matrix |A:y| and reduce it. Hope this helps if it's not already too late
__________________
Mechanical Engineers build weapons. Civil Engineers build targets.
yatzr is offline  
 

Tags
matrix, problems, word

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On



All times are GMT -8. The time now is 01:28 AM.

Tilted Forum Project

Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2024, vBulletin Solutions, Inc.
Search Engine Optimization by vBSEO 3.6.0 PL2
© 2002-2012 Tilted Forum Project

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360